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作者：Bungert, Leon; Calder, Jeff; Roith, Tim
作者单位：University of Wurzburg; University of Minnesota System; University of Minnesota Twin Cities; Helmholtz Association; Deutsches Elektronen-Synchrotron (DESY)
摘要：In this paper we prove the first quantitative convergence rates for the graph infinity Laplace equation for length scales at the connectivity threshold. In the graph-based semisupervised learning community this equation is also known as Lipschitz learning. The graph infinity Laplace equation is characterized by the metric on the underlying space, and convergence rates follow from convergence rates for graph distances. At the connectivity threshold, this problem is related to Euclidean first pa...
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作者：Lodewijks, Bas; Ortgiese, Marcel
作者单位：University of Augsburg; University of Bath
摘要：We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the network, so that a new vertex connects to one of the old vertices with a probability that is proportional to their vertex-weight. We first identify the asymptotic degree distribution of a uniformly chosen vertex for a general vertex-weight distribution. For...
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作者：Movassagh, Ramis; Szegedy, Mario; Wang, Guanyang
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：Sourav Chatterjee, Persi Diaconis, Allan Sly, and Lingfu Zhang (Ann. Probab. 50 (2022) 1-17), prompted by a question of Ramis Movassagh, renewed the study of a process proposed in the early 1980s by Jean Bourgain. A state vector v is an element of R-n, labeled with the vertices of a connected graph, G, changes in discrete time steps following the simple rule that at each step a random edge (i, j) is picked and v(i) and v(j) are both replaced by their average (v(i) + v(j))/2. It is easy to see ...
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作者：Gundlach, Rowel; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：We analyse the cluster discovered by invasion percolation on a branching process with a power-law offspring distribution. Invasion percolation is a paradigm model of self-organised criticality, where criticality is approach without tuning any parameter. By performing invasion percolation for n steps, and letting n -> infinity, we find an infinite subtree, called the invasion percolation cluster (IPC). A notable feature of the IPC is its geometry that consists of a unique path to infinity (also...
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作者：Izyurov, Konstantin; Kemppainen, Antti; Tuisku, Petri
作者单位：University of Helsinki
摘要：We compute rigorously the scaling limit of multipoint energy correlations in the critical Ising model on a torus. For the one -point function, averaged between horizontal and vertical edges of the square lattice, this result has been known since the 1969 work of Ferdinand and Fischer. We propose an alternative proof, in a slightly greater generality, via a new exact formula in terms of determinants of discrete Laplacians. We also compute the main term of the asymptotics of the difference E(EV ...
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作者：Atar, Rami; Castiel, Eyal; Reiman, Martin I.
作者单位：Technion Israel Institute of Technology; Columbia University
摘要：The standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC), which assumes that the underlying static allocation linear program (LP) is critical and has a unique solution. This solution determines the graph of basic activities, which identifies the set of activities (i.e., class-server pairs) that are operational. In this paper we explore the extended HTC, where the LP is merely assumed to be critical. Because multiple so...
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作者：Landim, Claudio; Misturini, Ricardo; Sau, Federico
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal do Rio Grande do Sul; University of Trieste
摘要：Let E-n subset of R-d, n >= 1, be a sequence of finite sets and consider a E-n-valued, irreducible, reversible, continuous-time Markov chain (X-t((n)):t >= 0). Denote by P(R-d) the set of probability measures on R-d and by I-n:P(R-d)->[0,+infinity) the level two large deviations rate functional for X(t )((n))as t ->infinity. We present a general method, based on tools used to prove the metastable behaviour of Markov chains, to derive a full expansion of InIn expressing it as I-n=I-(0)+& sum;(1...
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作者：Biskup, Marek; Krieger, Andrew
作者单位：University of California System; University of California Los Angeles
摘要：We consider a long-range percolation graph on Z(d) where, in addition to the nearest-neighbor edges of Z(d) , distinct x,y is an element of Z(d) are connected by an edge independently with probability asymptotic to beta|x - y|(-s), for s is an element of (d, 2 d) , beta > 0 and |center dot| a norm on R-d. We first show that, for all but perhaps a countably many beta > 0, the graph-theoretical (a.k.a. chemical) distance between typical vertices at |center dot|-distance r is, with high probabili...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：It is known since (Theory Probab. Appl. 11 (1966) 390-406) that the slow motion X-epsilon in the time-scaled multidimensional averaging setup dX(epsilon)(t)/dt = 1/epsilon B(X-epsilon(t), xi(t/epsilon(2))) +b(X-epsilon(t), xi(t/epsilon(2))), t is an element of [0, T] converges weakly as epsilon -> 0 to a diffusion process provided EB(x, xi(s)) 0 where xi is a sufficiently fast mixing stochastic process. In this paper we show that both X-epsilon and a family of diffusions Xi(epsilon) can be red...
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作者：Kramkov, Dmitry; Sirbu, Mihai
作者单位：Carnegie Mellon University; University of Texas System; University of Texas Austin
摘要：We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan. and an optimal maximal S-monotone set G are characterized by the condition that the support of. is contained in the graph of the S-projection on G. For a Gaussian random variable Y, we get a unique decomposition: Y = X+ Z,...
